To increase the precision of coordinate measuring apparatus, it has been known for some time to provide the measuring results with computed corrections. The measuring results are the coordinate measuring values which are supplied by the scales in the measurement axes of the apparatus. An overview of different corrective methods, which are utilized for this purpose, are disclosed, for example, in U.S. Pat. No. 5,594,668, incorporated herein by reference. In this patent, errors are corrected which are caused by the dynamic deformation of the structure of the apparatus because of the acceleration of the measurement sleds and the mass inertia of the moved parts. Even though the measurement errors of the apparatus are substantially reduced with the above-described corrective methods and the measurement accuracy is significantly increased, there still remain, with respect to specific tasks, residual errors which cannot simply be neglected.
For example, and because of the improved capability of individual system components, coordinate measuring apparatus are presently used increasingly also to make form measurements and to determine position features on circularly-shaped and cylindrically-shaped geometric elements. However, the unreliability of the measurement for the determination of form deviations with a coordinate measuring apparatus is still considerably greater than for conventional form measuring apparatus for circular forms, cylindrical forms and spherical forms. The reasons are essentially associated with the measuring system dynamic and the apparatus dynamic. Residual errors which can hardly be corrected or can be corrected only with considerable effort are also reasons causing the unreliability in measurements. The residual errors result from the dynamic of the displacement movements of the measurement sleds of the coordinate measuring apparatus. Errors having a maximum second order and which are caused by centrifugal force are described in the above-mentioned U.S. Pat. No. 5,594,668. In addition to these errors, errors of higher orders occur such as drag errors, vibrations of the controller which is intended to hold the measuring force constant et cetera. These errors are systematic and reproducible but cannot be described by a simple mathematical relationship. In addition, the error performance of the apparatus during its service life can change, inter alia, because of changing thermal influences, mechanical stress and wear as well as because of changes of the characteristic lines of the electronic components in the control and the drives of the apparatus such as after an exchange of such components.